During taxi, what are the regulation(s) that apply to opening an overhead bin or a galley storage container to put something away?
When a crewmember is performing a safety-related duty, exceptions to the regulation/policy are permissible. As noted, the cabin and galleys must be secure prior to pushback, takeoff, and landing. If a crewmember needs to perform a safety demonstration and the demo kit’s approved stowage location is in an overhead bin, which is typical, crewmembers are permitted to retrieve and stow the equipment as needed.
Rather than paraphrase the content, it’s best to read the regulations and guidance involved in their full content:
See paragraphs (b), (c) and sub‐paragraphs, (d), and (e). While it doesn’t explicitly state a flight attendant can open/close a bin if the task being performed is safety-related, yet sometimes we need to read between the lines to understand the intent of the regulation.
From 8900.1 Volume 3, Chapter 33, Section 6, see paragraph 3‐3550 Retention of Items of Mass.
Also in 8900.1 Volume 3, Chapter 33, Section 6, see paragraph 3568, E. Phases of flight.
Collectively, the regulation and 8900.1 guidance bring light to the permissibility for flight attendants to open and close overhead bins and storage containers to secure the aircraft during taxi.